
Although joint angle is commonly computed from the coordinates of the joint centers as a userangle (see the UserAngle Issues section for the details), it can be also computed from the relative orientation angles of the joint. In 1DOF joints such as the hinge joint, the joint angle corresponds to one of the orientation angles and no additional computation is required. But in joints with more than 1 DOF, additional computation must be performed to obtain the joint angle. From [6] of Computation of the Orientation Angles:
where T_{D/P} = the transformation matrix from the proximal reference frame to the distal reference frame at a joint, and = the relative orientation angles between the segments at the joint. Now, let's assume that the Z axes of the segmental reference frames coincide with their respective longitudinal axes of the segments:
and
where s = the unit vector of a segment's longitudinal axis. As one can see in [3], the longitudinal axis vector of the distal segment described in the proximal reference frame has nothing to do with angle because it is the rotation angle about the Z axis. The angle between the longitudinal axes of the proximal and distal segments forming a joint () can be computed from the scalar product of the two s vectors: from [2] and [3],
Thus, the joint angle is

© YoungHoo Kwon, 1998 